组合脉冲压裂加载过程耦合模拟及火药配比影响敏感性分析

基于组合脉冲压裂物理过程,以三种燃速火药柱串联、中心管同步点燃方式,结合火药爆燃加载、压挡液柱运动、射孔孔眼泄流、裂缝起裂、高压气体裂缝内流动及裂缝扩展等子模型,组建多级爆燃压裂耦合模拟模型。并据此分析不同配比火药组合爆燃压裂时,井底压力变化及裂缝延伸情况。结果表明:不同燃速火药串联组合可实现一级火药快速爆燃,瞬间达到多方向射孔孔眼起裂压力,二、三级火药持续长时间燃烧维持高压以充分延伸裂缝的目的;在确定一级快速火药和总火药用量后,井底爆燃压力加载速率和各方向破裂压力均随第三级燃速火药质量比重的增加而呈现降低趋势,但变化不明显;而不同方向裂缝最终延伸长度对二、三级燃速火药的配比具有较强敏感性;在以多方向裂缝安全起裂为目标、设定一级燃速火药后,合理配比三种火药比单一配比高-中速、高-低速火药,可更有效地延长爆燃压裂过程的井底有效持压时间,从而可大幅扩展火药用量上限,提高爆燃压裂裂缝延伸规模。     

多孔线性控制套筒致裂效果影响因素分析

针对坚硬难垮落顶板弱化问题,在分析多孔线性控制套筒致裂机理的基础上,建立700mm×300mm×400mm试块。通过套筒致裂压力及钻孔孔壁周围应变变化情况,分析孔壁周围应力大小、分布及应力集中现象,研究钻孔直径、孔间距、套筒致裂压力对应力集中现象的影响,同时分析这三者对裂纹扩展方向的影响,得出套筒致裂最优法。试验结果表明:(1)套筒致裂效果受钻孔直径、孔间距和套筒压力等综合因素影响,采用大直径、大间距的布孔方式可获得较好的致裂效果;(2)多孔线性控制致裂试验的张性裂缝扩展方向主要沿着各钻孔中心连线方向;(3)钻孔直径30mm、间距300mm的试块致裂压力为18.6MPa,远大于顶板岩体抗拉强度,将套筒致裂法应用于顶板弱化是可行的。本研究对解决采空区坚硬顶板大面积悬顶具有理论意义和应用价值。     

光弹贴片法在混凝土裂缝扩展过程研究中的应用

采用光弹性贴片法对平面尺寸为３．６×３．０，３．０×２．５，２．４×２．０，１．８×１．５，１．２×１．０，０．６×０．５ｍ＾２的巨型紧凑拉伸试件预制裂缝的起裂，稳定扩展至失稳破坏的全过程进行了系统的研究，实验结果表明，在试件高达１米以上的实验范围内，失稳破坏前裂缝稳定扩展长度几乎是一个稳定的常数值，且与试件初始缝长ａｏ无关。还发现，宏观裂缝的起裂早晚与初始缝长ａ０有关。     

基于扩展有限元法的混凝土断裂参数研究

基于扩展有限元法(XFEM),对混凝土三点弯曲梁的开裂过程进行数值模拟,获得加载全过程的荷载-裂缝口张开位移(P-CMOD)曲线以及裂缝扩展过程;对比数值模拟和试验获得的P-CMOD曲线发现,二者比较吻合,验证了数值模型的可靠性;通过XFEM和电子散斑干涉技术获得整个加载过程的断裂过程区(FPZ)长度,二者吻合程度较高,表明XFEM可用于预测FPZ长度;基于XFEM分析了初始缝高比对混凝土断裂参数的影响。结果表明:FPZ长度随着裂缝的扩展而增加,当FPZ完全发展后,其长度逐渐减小;峰值荷载时和发展完全时的FPZ长度均随初始缝高比的增大而减小;随着初始缝高比的增大,起裂韧度KIicn i基本不变,失稳韧度KIucn和临界裂缝尖端张开位移(CTODc)呈减小趋势。     

致密油藏动态裂缝扩展机理及应用

致密油藏采用注水吞吐补充地层能量取得了一定效果. 但多轮次注水吞吐后, 地层压力和产量降低快. 本文考虑了致密油藏复杂的裂缝形态, 根据艾尔文理论及弹性力学剖析I型裂缝尖端附近的应力场分布, 基于渗流力学、裂缝性致密油藏特征及动态裂缝渗流规律, 建立了多裂缝交叉裂缝扩展渗流模型, 结合注水诱导裂缝扩展机理及断裂力学能量守恒原理, 得到裂缝扩展长度. 依据致密油藏逆向渗吸原理, 提出将注水吞吐转为不稳定脉冲注水. 对比分析注水吞吐、脉冲注水2种能量补充发方式, 预测10年累计采油、压力及剩余油分布. 结果表明, 裂缝净内压随着注水量的增加而升高, 当应力场强度因子达到断裂韧度, 在裂缝尖端会发生扩展. 扩展及延伸的天然裂缝相互沟通, 呈现不规则复杂缝网, 在复杂缝网中主要发生逆向渗吸作用. 脉冲注水累计产油高、注水波及面积广、逆向渗吸作用强. 裂缝性致密油藏水平井注水吞吐转变为脉冲注水方式, 能够充分发挥动态缝网的逆向渗吸及线性驱替作用, 实现有效驱油的目的.      

岩石偏心圆孔单裂纹平台圆盘的动态裂纹扩展与止裂

针对平台圆环构型的优点, 提出偏心圆孔单裂纹平台圆盘(cracked eccentrically holed flattened disc, CEHFD), 该试样具有更长的断裂路径。利用霍普金森压杆加载系统, 径向冲击CEHFD试样, 完成Ⅰ型动态断裂实验。砂岩试样表面粘贴应变片和裂纹扩展计, 用于监测裂纹动态起裂、扩展和止裂的全过程。实验表明, 在整个断裂过程中, 裂纹非匀速扩展, 裂纹扩展速度在裂纹起裂后加速上升, 在裂纹止裂前有明显的减速, 与地震时断层的动态破裂全过程完全吻合。采用实验-数值-解析法得到动态应力强度因子, 其时间历程呈现先增大后减小的趋势。根据断裂过程不同时刻, 得到相应的动态起裂韧度、扩展韧度及止裂韧度。在动态断裂全过程中, 动态扩展韧度为速度的函数, 变化趋势与速度一致, 随着时间先增大后减小; 动态起裂韧度大于动态止裂韧度, 止裂韧度随着裂纹最大扩展速度的增大而降低, 并且有较大的离散性。     

冲击加载下巷道内裂纹的扩展特性及破坏行为

为了开展含预制裂纹的巷道模型试样在冲击载荷下的动态断裂响应实验,选用青砂岩作为模型材料制作巷道模型试样,以可调速落锤冲击实验机作为冲击加载装置进行试样的动态断裂实验,分析冲击载荷作用下的巷道内裂纹的扩展规律。采用裂纹扩展计及应变片测试系统监测裂纹的起裂时间、扩展速度及止裂时间,并借助于AUTODYN、ABAQUS有限元数值分析软件对实验模型进行数值模拟,计算裂纹的动态起裂韧度、动态扩展韧度、动态止裂韧度等断裂参数。结果表明:巷道内裂纹在扩展路径过程中存在着明显的止裂现象;采用实验-数值方法能够较好地得出裂纹的起裂韧度、扩展韧度和止裂韧度等参数。另外,对止裂现象进行了初步的分析,讨论了试样内应力反射波与透射波对止裂问题的影响。     

PMMA材料裂纹动态扩展及止裂研究

PMMA俗称有机玻璃,是一种用途十分广泛的工程材料,其裂纹动态扩展及止裂是工程应用研究的难点问题。以SHPB为动态加载装置,通过实验和仿真研究了含圆孔PMMA板的单边裂纹动态扩展问题,模拟结果与裂纹动态实验结果的对比验证了仿真模型的有效性。在此基础上,研究了PMMA板中的圆孔半径、预裂纹长度、止裂孔半径、止裂孔与裂纹尖端竖直位移等因素对裂纹扩展的影响。研究结果表明,圆孔半径和预裂纹长度对裂纹的起始扩展时间有明显影响,在裂纹尖端设置止裂孔可以有效地抑制裂纹的扩展,并且止裂孔半径、止裂孔与裂纹尖端竖直位移对止裂效果有显著影响。本文研究结果对PMMA材料工程应用有一定的参考价值。     

混凝土三点弯曲梁裂缝断裂全过程数值模拟研究

考虑裂缝黏聚力的作用,基于Paris位移公式推导出混凝土三点弯曲梁裂缝扩展过程中断裂过程区上的裂缝张开位移的解析表达式.采用起裂韧度作为裂缝起裂及扩展的判断标准,提出了荷载作用下混凝土裂缝起裂、扩展及失稳破坏全过程的数值模拟方法,并分别与国内外断裂试验实测值及有限元计算值进行了比较.结果表明,本文提出的数值模拟方法形式简单且精度较好.     

水平地应力差对周期注水应力改造水力压裂影响的试验研究

为揭示地应力环境对周期注水应力改造提高压裂效果的影响规律,以黑龙江双鸭山矿区煤系页岩为研究对象,克服煤系页岩非均质性,利用相似比制作型页岩试件,开展了实验室真三轴水力压裂试验。利用声发射技术监测裂缝起裂和扩展特征,通过RA-AF散点分布特征给出了应力改造和压裂阶段主导裂缝类型,分析得到了周期注水应力改造下水平地应力差对裂缝特征以及裂缝起裂、扩展的影响规律,提出了起裂阶段与扩展阶段声发射判断指标。试验结果表明:应力改造阶段裂缝起裂与扩展以微裂缝为主,剪切型微裂缝占比波动上升,第2个周期裂缝主频范围最大,裂缝发育最为活跃;压裂阶段裂缝起裂与扩展以宏观裂缝为主,张拉型裂缝占比呈增加趋势,当水平地应力差与注水压力接近2.0MPa时,张拉型裂缝占比最大,分布范围最广,压裂效果最显著。另外,本文提出了裂缝起裂与扩展阶段声发射判断指标为平均声发射能率k。k降幅在37.74%以上时,裂缝由起裂阶段进入扩展阶段。周期注水应力改造可以减小水平地应力差对裂缝扩展的约束能力,促进微裂缝大量发育、沟通天然裂缝形成缝网,从而提高页岩气开采率。     

Stability of Discrete Stokes Operators in Fractional Sobolev Spaces

Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations for the time-dependent Stokes equations with a source term in L ^p (0, T; L ^q (Ω)) and prove uniform estimates on the time derivative and discrete Laplacian of the discrete velocity that are similar to those in Sohr and von Wahl [20]. On long leave from LIMSI (CNRS-UPR 3251), BP 133, 91403, Orsay, France.     

SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＳＩＮＧＵＬＡＲ　ＰＥＲＴＵＲＢＡＴＩＯＮＳ　ＦＯＲ　Ａ　ＣＬＡＳＳ　ＯＦ　ＢＯＵＮＤＡＲＹ　ＶＡＬＵＥ　ＰＲＯＢＬＥＭＳ　ＯＦ　ＨＩＧＨＥＲ　ＯＲＤＥＲ　ＮＯＮＬＩＮＥＡＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...     

An Example of Finite-time Singularities in the 3d Euler Equations

Let be the exterior of the closed unit ball. Consider the self-similar Euler system

大型爆炸防护结构的动态应力测试与分析

对某大型爆炸防护结构进行不同工况的爆炸实验,通过电测法测量了几个典型位置的应力,结果 显示:从第1和第2主应力测试结果来看,球壳表面在爆炸冲击作用下的冲击应力峰值除第1次最大外,之后 基本以拉压应力状态来回振动,而且振动应力在经过1~2个来回后立刻减小到100 MPa以下,土的堆压可 以起到削弱球壳振动的作用,因此球壳单次爆炸引起的振动疲劳问题大为削弱;模型的强度满足设计要求;排 气孔附近是应力最为集中区域;炸药的形状系数对结构的安全影响很大。     

Approximate representations and pointwise bounds for solutions of a class of non-linear boundary value problems

This article establishes an approximation in the implicit form (within the limits of error) of solutions of [L + M(ε)]x = ρ(t, x) satisfying the limiting conditions x^(2k)(0) = x^(2k+1)(τ) = 0, k = 0,1,…, n?1, L being a linear differential operator of degree equal to 2n with constant coefficients and M(ε) a differential operator of an inferior order enabling the absorption terms and the coefficients to vary slowly. f(t,x) is continuous in the sense of Lipschitz, not negative, monotonous, increasing in x and of the saturation type.     

On the sensitivity of interconversion between relaxation and creep

The interconversion equation of linear viscoelasticity defines implicitly the interrelations between the relaxation and creep functions G(t) and J(t). It is widely utilised in rheology to estimate J(t) from measurements of G(t) and conversely. Because different molecular details can be recovered from G(t) and J(t), it is necessary to work with both. This leads naturally to the need to identify whether it is better to first measure G(t) and then determine J(t) or conversely. This requires an understanding of the stability (sensitivity) of the recovery of J(t) from G(t) compared with that of G(t) from J(t). Although algorithms are available that work adequately in both directions, numerical experimentation strongly suggests that the recovery of J(t) from G(t) measurements is the more stable. An elementary theoretical rationale has been given recently by Anderssen et al. (ANZIAM J 48:C346–C363, 2007) for single exponential models of G(t) and J(t). It explicitly exploits the simple algebra of such functions. In this paper, corresponding bounds are derived that hold for arbitrary sums of exponentials. The paper concludes with a discussion, from a practical rheological perspective, about the implications and implementations of the results.     

On the stability of penny-shaped cracks with friction: the five types of brittle behavior

The theory of penny-shaped cracks has been the subject of numerous investigations because of its conceptual simplicity and the feasibility of obtaining mathematical solutions. The simplicity of many of the final results makes the theory useful in many applications. This paper addresses a gap in the theory, the effect of interfacial friction in closed cracks and, in particular, its influence on the most unstable crack orientation and, hence, the compressive strength of materials. When friction is accounted for it is found that five types of brittle behavior are possible: (a) mode-I opening, (b) mixed opening and shear, (c) pure-shear without friction, and (d) shear with interfacial friction. A fifth type of behavior (e) which corresponds to a stable material response occurs when the compressive traction on the crack is so large that friction inhibits crack growth. The first four types, namely, (a), (b), (c), (d) result in incipient material failure. The range of stress states for which each of the failure (incipient) types applies is given explicitly. Failure of a brittle material under triaxial test conditions is considered in detail to illustrate the results. An experiment performed by Howe et al. [Howe, P.M., Gibbons, G.G., Webber, P.E., 1985. An experimental investigation of the role of shearing initiation of detonation. In: Short, J.M. and Deal, W.E. (Eds.), Proceedings of the 8th International Symposium on Detonation, Albuquerque, NM] showing the response of a brittle material (TNT) to impact illustrates (perhaps surprisingly) behavior of types (c) and (d). The chemical sensitivity of the TNT allows us to observe the effect of friction better than would be possible in a non-reactive material. The conditions that allow crack growth within the crack plane are discussed briefly.     

Molecular dynamics studies on the local disordering of Σ3 and Σ11 grain boundaries in aluminium bicrystal

Molecular dynamics (MD) simulations using Morse interaction potential are performed in studies of [110] symmetrical tilt grain boundary (GB) structures with mis-orientation angles 50.5°(Σ11), 129.5°(Σ11), 70.5°(Σ3) and 109.5°(Σ3) at various tempratures. The GB structures are found to start local disordering at about 0.5T _m (T _m is the melting point of aluminium) for 50.5°(Σ11), 0.32T _m for 129.5° (Σ11) and 0.38T _m for 70.5°(Σ3), respectively. These results agree with conclusions deduced from the anelastic measurements. But, for twin-boundary structure 109.5°(Σ3), this disordering has not been found even when temperature increases up to 0.9T _m . The project supported by the National Natural Science Foundation of China and Laboratory for Non-linear Mechanics of Continuous Media, Institute of Mechanics, Academia Sinica.     

On a dynamical system on matrix algebra

LetM(n) be the algebra of alln×n complex matrices. We consider a dynamical system onM(n) defined by the vector fieldV(X)=[[X ^*,X],X], (X M(n)). It arises as the gradient flow for two kinds of variational problems onM(n). Given anyX ₀ M(n), letX(t) be the trajectory starting atX ₀. We study the global behavior ofX(t) ast . We show that, ifX ₀ is semisimple, thenX(t) converges exponentially to a normal matrix. IfX ₀ is not semisimple, then the behavior ofX(t) is completely different and difficult to analyze. We give some results also in this case. Furthermore, we discuss about a center manifold approach to our dynamical system.     

Deduction of Saint-Venant"s Principle for the Asymptotic Residue of Elastic Rods

Let u(ε) be a rescaled 3-dimensional displacement field solution of the linear elastic model for a free prismatic rod Ω^ε having cross section with diameter of order ε, and let u ⁽⁰⁾ –Bernoulli–Navier displacement – and u ⁽²⁾ be the two first terms derived from the asymptotic method. We analyze the residue r(ε) = u(ε) − (u ⁽⁰⁾ + ε² u ⁽²⁾) and if the cross section is star-shaped, we prove such residue presents a Saint-Venant"s phenomenon near the ends of the rod. This revised version was published online in August 2006 with corrections to the Cover Date.